Ulam–Hyers stability for hybrid differential equations with mixed fractional derivatives and the μ -Laplacian operator

Source abstract

Abstract In this work, we investigate the Ulam–Hyers stability and generalized Ulam–Hyers stability for a class of hybrid differential equations involving both proportional fractional derivatives and classical derivatives, coupled with the μ -Laplacian operator and subject to fractional integral boundary conditions. Building upon recent existence results for this class of equations, we establish sufficient conditions under which solutions exhibit Ulam–Hyers stability. The analysis relies on nonlinear analysis techniques and properties of the μ -Laplacian operator. Two illustrative examples are provided: one for classical Ulam–Hyers stability and another for uniform stability under a variable perturbation described by a power-type control function.